Optimization of average grain size and grain size distribution is important for many commercial products utilizing advanced materials. Advanced materials can be found in semiconductor and electronic devices, high power components, structural alloys and ceramics, and high performance coatings. Grain size and grain size distribution is particularly critical for improving performances of semiconductor materials.
Conventional grain size analysis utilizes techniques such as micrograph image analysis, which is often referred to as metallography. The micrograph image analysis is generally performed upon micrographs of carefully polished and preferentially etched polycrystalline samples. However, the polishing and etching processes are very destructive to protective layers over-coating the samples. Moreover, the micrographs so taken reflect merely 2-dimensional cross-sectional views of the 3-dimensional crystal grains, rendering determination of grain size based thereupon inaccurate. Finally, the resolution limits of the equipments currently available render the micrograph image analysis suitable only for materials with relatively large grains, usually above 5 microns.
More recently developed grain size analysis techniques employ electron backscatter diffraction (EBSD) and focused ion beam (FIB) systems to measure grain sizes as small as about 0.25 microns. Although these new techniques are more accurate than the conventional micrograph image analysis, they are slow and tedious to carry out, because they can measure only one grain at a time. In order to obtain statistically accurate analysis results, a reasonably large number of grains have to be analyzed one by one, and conducting a complete analysis is therefore too slow for practical on-line quality control applications. Moreover, the EBSD and FIB techniques both require destructive polishing and cleaning, and they also measure only cross-sectional areas of the grain, not its full volume.
Ultrasonic and optical reflection techniques have also been used to estimate average crystallite size by using a calibrated sample. However, measurements obtained by such techniques are easily distorted by variation in numerous non-relevant material properties of the polycrystalline samples, such as phase composition crystallographic texture, residual stress, porosity, etc. Therefore, the ultrasonic and optical reflection techniques cannot accurately measure average grain size unless all other material properties are always constant, which rarely happens. These techniques are not capable of measuring grain size distribution.
X-ray diffraction (XRD) techniques have also been used to determine the relative crystallite size and size distribution of a polycrystalline material. A beam of monochromatic x-rays, when directed to a polycrystalline material surface, scatters in all directions. The scattered x-rays in certain directions interfere and reinforce each other, resulting in diffraction peaks (i.e. intensity maxima) in such directions. Each particular set of crystalline planes (hkl) of a grain has an associated diffraction peak that occurs at a particular angle. Therefore, the diffraction image provides direct information about the total number and spacing of individual crystal grains that comprise the polycrystalline material. Based on such information, average grain size and grain size distribution can be determined.
Peak broadening analysis, which is also referred to as line profile analysis or line broadening analysis, is a commonly used x-ray diffraction method for determining relative crystallite size. This method observes the change in peak width of an x-ray diffraction peak for a particular (hkl) crystallographic plane. A diffraction peak typically results from a large number of grains of different sizes within the irradiated area on the sample satisfying the Bragg diffraction condition. As the average grain size decreases, the x-ray diffraction peak width (i.e. the distance between two adjacent diffraction peaks) increases, and thus peak width can be used to measure the relative change in average grain size.
However, the peak broadening analysis is suitable only for analyzing polycrystalline materials with grain sizes generally below 0.1 micron. It is inadequate when the polycrystalline materials to be measured have grains of larger sizes. Moreover, the diffraction peak width can be significantly affected by variation in irrelevant factors such as instrument broadening effects (i.e. focusing precision of the x-ray optics), crystallographic texture, and presence of faults in crystallographic structure including dislocations. The peak broadening analysis is effective only under tightly controlled comparative analysis conditions, which require very similar sample compositions and cold work levels with measurements conducted on the same instrument. Therefore, the peak broadening analysis is of very limited use for most advanced thin film materials that have widely varying compositions and grain sizes (commonly >0.1 micron), substantial degree of texture, and residual micro and macro-strains.
Another less common x-ray diffraction method for grain size analysis involves the analysis of “spot” reflections from individual grains, which are bright spots formed on x-ray film or a two-dimensional detector by diffracted x-rays with high intensity. This x-ray diffraction method has been referred to as spot count analysis. Generally, a correlation exists between the total number of such bright spots counted with a known total irradiated volume and the average grain size of the sample material, assuming that each spot is formed by x-ray diffracted by an individual grain. It is also well established that the spot intensity is proportional to the size of the grain from which the x-ray is diffracted. Thus, the distribution of spot intensities can be correlated to the distribution of grain sizes.
The spot count analysis is limited in practice to a certain grain size range due to resolution and sensitivity limits of equipment used, and is usually only suitable for analyzing materials with grain sizes above 1 micron. Although a paper by Horst Ebel entitled “Crystallite Size Distributions from Intensities of Diffraction Spots”, POWDER DIFFRACTION, Vol. 3, No. 3, September 1988, pp. 168-71, states that the spot count analysis theoretically can analyze non-textured polycrystalline material with crystallite size as small as 0.1 micron, actual data presented by this paper are only for aluminum powders with sizes ranging from 9.5 to 11 microns. Moreover, accuracy of the spot count analysis is also adversely affected by the presence of any crystallographic texture. As the texture increases, more crystal grains tend to orient themselves in just a few highly preferred orientations, which results in overlapping of spot reflections on several predominant regions on the x-ray film, making it more difficult to resolve spots in these regions. Furthermore, the correlation between the number of spots counted within the known irradiated volume and the average grain size can be complicated by the presence of crystallographic texture. The spot analysis technique therefore can only be used to analyze completely non-textured fine spherical powders, with completely random crystal orientations. There are no known practical solutions as to how the spot analysis technique can be used for analyzing continuous polycrystalline materials with any degree of texture and/or residual stress present, nor as to how such technique can be used to provide grain size distribution information.
It therefore is one object of the present invention to provide a method and apparatus for rapid determination of average grain size and grain size distribution in polycrystalline materials with widely varying grain sizes (from about 0.1 micron to about 100 microns) and varying amounts of crystallographic texture and residual stress.
It is another object of the invention to provide a system enabling sufficiently rapid grain size measurement to allow automated grain size analysis production quality control in commercial processing operations.
A further object of the present invention is to provide a grain size analysis system that can be operated in a production environment, and by persons without specialized skill or training.
Other objects and advantages will be more fully apparent from the ensuing disclosure and appended claims.